Relative entropy and curved spacetimes

Ciolli, Fabio; Longo, Roberto; Ranallo, Alessio; Ruzzi, Giuseppe

doi:10.1016/j.geomphys.2021.104416

Cited by 21 publications

(6 citation statements)

References 30 publications

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“…It should be noticed that (9) also appeared in [30], (A.5), apparently computed by using the q-numbers [n] q (see also e.g., [23]). Unfortunately, it is unclear how (A.5) in [30] is derived and, in addition, any computation of the q-grand partition function using the [n] q numbers does not reproduce (9).…”

Section: The Grand Partition Function Of Quons: One-modementioning

confidence: 99%

“…Another direction, indeed connected with applications to the previous questions of quantum field theory, and also involving applications which are certainly relevant for the applied sciences, such as quantum information theory and quantum computing, is the detailed study of the von Neumann entropy and the Araki relative entropy, see for example [ 7 , 8 , 9 ] for the foundations and recent results.…”

Section: Introductionmentioning

confidence: 99%

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On the Thermodynamics of the q-Particles

Ciolli

Fidaleo

2022

Entropy

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Since the grand partition function Zq for the so-called q-particles (i.e., quons), q∈(−1,1), cannot be computed by using the standard 2nd quantisation technique involving the full Fock space construction for q=0, and its q-deformations for the remaining cases, we determine such grand partition functions in order to obtain the natural generalisation of the Plank distribution to q∈[−1,1]. We also note the (non) surprising fact that the right grand partition function concerning the Boltzmann case (i.e., q=0) can be easily obtained by using the full Fock space 2nd quantisation, by considering the appropriate correction by the Gibbs factor 1/n! in the n term of the power series expansion with respect to the fugacity z. As an application, we briefly discuss the equations of the state for a gas of free quons or the condensation phenomenon into the ground state, also occurring for the Bose-like quons q∈(0,1).

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Section: The Grand Partition Function Of Quons: One-modementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

On the Thermodynamics of the q-Particles

Ciolli

Fidaleo

2022

Entropy

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“…Motivated by the Bisognano-Wichmann property (BW) in AQFT, the modular flow, namely the flow of the one-parameter group generated by an Euler element on a causal homogeneous space M should be timelike future-oriented. Indeed, the modular flow is correspond to the inner time evolution of Rindler wedges (see [CR94] and also [BB99,BMS01,Bo09], [CLRR22,§3]). In our context this means that the modular vector field…”

Section: Wedge Domains In Causal Homogeneous Spacesmentioning

confidence: 99%

Covariant Homogeneous Nets of Standard Subspaces

Morinelli

Neeb

2021

Commun. Math. Phys.

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Rindler wedges are fundamental localization regions in AQFT. They are determined by the one-parameter group of boost symmetries fixing the wedge. The algebraic canonical construction of the free field provided by Brunetti–Guido–Longo (BGL) arises from the wedge-boost identification, the BW property and the PCT Theorem. In this paper we generalize this picture in the following way. Firstly, given a $$\mathbb Z_2$$ Z 2 -graded Lie group we define a (twisted-)local poset of abstract wedge regions. We classify (semisimple) Lie algebras supporting abstract wedges and study special wedge configurations. This allows us to exhibit an analog of the Haag–Kastler one-particle net axioms for such general Lie groups without referring to any specific spacetime. This set of axioms supports a first quantization net obtained by generalizing the BGL construction. The construction is possible for a large family of Lie groups and provides several new models. We further comment on orthogonal wedges and extension of symmetries.

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“…is the modular group of M(O), we are confronted with the problem to formulate sufficient conditions on O. As the specific examples in AQFT suggest, the modular flow on O should be timelike future-oriented ([TW97, BB99, BMS01, BS04, Bo09, LR08], [CLRR22,§3]), which in our context means that the modular vector field…”

Section: Introductionmentioning

confidence: 99%

Wedge domains in non-compactly causal symmetric spaces

Neeb¹,

Ólafsson²

2022

Preprint

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This article is part of an ongoing project aiming at the connections between causal structures on homogeneous spaces, Algebraic Quantum Field Theory (AQFT), modular theory of operator algebras and unitary representations of Lie groups. In this article we concentrate on noncompactly causal symmetric space G/H. This class contains the de Sitter space but also other spaces with invariant partial ordering. The central ingredient is an Euler element h in the Lie algebra of g. We define three different kinds of wedge domains depending on h and the causal structure on G/H. Our main result is that the connected component containing the base point eH of those seemingly different domains all agree. Furthermore we discuss the connectedness of those wedge domains. We show that each of those spaces has a natural extension to a non-compactly causal symmetric space of the form G C /G c where G c is certain real form of the complexification G C of G. As G C /G c is non-compactly causal it also comes with the three types of wedge domains. Our results says that the intersection of those domains with G/H agrees with the wedge domains in G/H.

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Relative entropy and curved spacetimes

Cited by 21 publications

References 30 publications

On the Thermodynamics of the q-Particles

On the Thermodynamics of the q-Particles

Covariant Homogeneous Nets of Standard Subspaces

Wedge domains in non-compactly causal symmetric spaces

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